Google defines paradox in three ways, the first two being:

  1. a statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory.

  2. a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true.

These are almost opposite definitions. My English book defined it as the second, but I've always understood it to mean the first. Which is the most common usage?

  • Good point! But this will be largely opinion based... or maybe someone can pull out some ngrams... but I would say (1) is the more common usage. – d'alar'cop Feb 15 '14 at 15:30
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    How paradoxical that 'paradoxical' should be defined paradoxically! – WS2 Feb 15 '14 at 15:32
  • There is no easy way to look this up in a corpus. One could try to come up with a bunch of obvious collocations clearly identifying either meaning, but that is not trivial, and only an approximation. To be completely sure, there's nothing one can do short of meticulously analysing every single occurrence of the word in the corpus. So while I am curious what kind of answers this produces, I am somewhat worried that we might end up with a handful of "I think X>Y" one-liners. So I am specifically asking people ahead of time to abstain from posting such comments as answers. – RegDwigнt Feb 15 '14 at 16:24
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    They both refer to an implicit and unexplained contradiction between two viewpoints, both of which seem valid. The first one is more formal, and simply recapitulates the last two lines of the truth table for P ⊃ Q, which is what licenses proof by contradiction. The second one is more experiential, and contrasts one's ordinary presuppositions with actual objective observation. Both give a confused feeling, of looping back and forth between two incompatible predictions. Similar to visual tricks like seeing different faces in a drawing; you can't ever see both of them at the same time. – John Lawler Feb 15 '14 at 17:43

I don't see the definitions as contradictory. Both cases illustrate the central concept of paradox, which is extreme disjunct between A:common sense/received opinion and B:logic/reasoning.

You could say a paradox is like a fight, or a sporting contest. The only real difference between OP's two definitions is that if we (the "spectators") support A (common sense), then definition #1 applies.
If we support B (logic), it's definition #2.

It's not that different to the underlying principle of Swift's A Modest Proposal (that the poor Irish could solve their economic woes by selling their children as food to the rich English). In both cases, two incompatible perspectives/methodologies are being applied, giving contradictory conclusions.

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